TY - GEN
T1 - Succinct permanent is NEXP-hard with many hard instances (extended abstract)
AU - Dolev, Shlomi
AU - Fandina, Nova
AU - Gutfreund, Dan
N1 - Funding Information: Partially supported by the Israeli Ministry of Science (Russia Israel grant), Rita Altura Trust Chair in Computer Sciences, Lynne and William Frankel Center for Computer Sciences, Israel Science Foundation (grant number 428/11), Cabarnit Cyber Security MAGNET Consortium, Grant from the Technion’s Institute for Future Defense Technologies Research named for the Medvedi, Shwartzman and Gensler families, and the Israeli Internet Association.
PY - 2013/9/9
Y1 - 2013/9/9
N2 - The main motivation of this work is to study the average case hardness of the problems which belong to high complexity classes. In more detail, we are interested in provable hard problems which have a big set of hard instances. Moreover, we consider efficient generators of these hard instances of the problems. Our investigation has possible applications in cryptography. As a first step, we consider computational problems from the NEXP class. We extend techniques presented in [7] in order to develop efficient generation of hard instances of exponentially hard problems. Particularly, for any given polynomial time (deterministic/probabilistic) heuristic claiming to solve NEXP hard problem our procedure finds instances on which the heuristic errs. Then we present techniques for generating hard instances for (super polynomial but) sub exponential time heuristics. As a concrete example the Succinct Permanent problem is chosen. First, we prove the NEXP hardness of this problem (via randomized polynomial time reduction). Next, for any given polynomial time heuristic we construct hard instance. Finally, an efficient technique which expands one hard instance to exponential set (in the number of additional bits added to the found instance) of hard instances of the Succinct Permanent problem is provided.
AB - The main motivation of this work is to study the average case hardness of the problems which belong to high complexity classes. In more detail, we are interested in provable hard problems which have a big set of hard instances. Moreover, we consider efficient generators of these hard instances of the problems. Our investigation has possible applications in cryptography. As a first step, we consider computational problems from the NEXP class. We extend techniques presented in [7] in order to develop efficient generation of hard instances of exponentially hard problems. Particularly, for any given polynomial time (deterministic/probabilistic) heuristic claiming to solve NEXP hard problem our procedure finds instances on which the heuristic errs. Then we present techniques for generating hard instances for (super polynomial but) sub exponential time heuristics. As a concrete example the Succinct Permanent problem is chosen. First, we prove the NEXP hardness of this problem (via randomized polynomial time reduction). Next, for any given polynomial time heuristic we construct hard instance. Finally, an efficient technique which expands one hard instance to exponential set (in the number of additional bits added to the found instance) of hard instances of the Succinct Permanent problem is provided.
UR - http://www.scopus.com/inward/record.url?scp=84883314535&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-38233-8_16
DO - 10.1007/978-3-642-38233-8_16
M3 - Conference contribution
SN - 9783642382321
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 183
EP - 196
BT - Algorithms and Complexity - 8th International Conference, CIAC 2013, Proceedings
T2 - 8th International Conference on Algorithms and Complexity, CIAC 2013
Y2 - 22 May 2013 through 24 May 2013
ER -